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Manuscript/seniority.tex
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@ -102,8 +102,9 @@ while higher sectors tend to contribute progressively less. \cite{Bytautas_2011,
In addition, sCI0 is size-consistent, a property that is not shared by higher orders of seniority-based CI.
However, already at the sCI0 level, $\Ndet$ scales exponentially with $\Nbas$, since excitations of all degrees are included.
Therefore, despite the encouraging successes of seniority-based CI methods, their unfavorable computational scaling restricts applications to very small systems. \cite{Shepherd_2016}
Besides CI, other methods that exploit the concept of seniority number have been pursued. \cite{Limacher_2013,Limacher_2014,Tecmer_2014,Boguslawski_2014a,Boguslawski_2015,Boguslawski_2014b,Boguslawski_2014c,Johnson_2017,Fecteau_2020,Johnson_2020,Henderson_2014,Stein_2014,Henderson_2015,Chen_2015,Bytautas_2018,Johnson_2022,Fecteau_2022}
\textcolor{red}{In particular, coupled cluster restricted to paired double excitations, which is the same as the antisymmetric product of 1-reference orbital geminals,
Besides CI, other methods that exploit the concept of seniority number have been pursued. \cite{Limacher_2013,Limacher_2014,Tecmer_2014,Boguslawski_2014a,Boguslawski_2015,Boguslawski_2014b,Boguslawski_2014c,Johnson_2017,Fecteau_2020,Johnson_2020,Johnson_2022,Fecteau_2022,Henderson_2014,Stein_2014,Henderson_2015,Chen_2015,Bytautas_2018}
\textcolor{red}{In particular, coupled cluster restricted to paired double excitations, \cite{Henderson_2014,Stein_2014,Henderson_2015} which is the same as the antisymmetric product of 1-reference orbital geminals,
\cite{Limacher_2013,Limacher_2014,Tecmer_2014,Boguslawski_2014a,Boguslawski_2015,Boguslawski_2014b,Boguslawski_2014c,Johnson_2017,Fecteau_2020,Johnson_2020,Johnson_2022,Fecteau_2022}
provides very similar energies as DOCI, and at a very favourable polynomial cost.}
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@ -144,8 +145,8 @@ The first one is physical.
We know that the lower degrees of excitations and lower seniority sectors, when looked at individually, often carry the most important contribution to the FCI expansion.
By combining $e$ and $s$ as is Eq.~\eqref{eq:h}, we ensure that both directions in the excitation-seniority map (see Fig.~\ref{fig:allCI}) are contemplated.
Rather than filling the map top-bottom (as in excitation-based CI) or left-right (as in seniority-based CI), the hCI methods fills it diagonally.
In this sense, we hope to recover dynamic correlation by moving right in the map (increasing the \textcolor{red}{seniority number} while keeping a low \textcolor{red}{excitation degree}),
at the same time as static correlation, by moving down (increasing the \textcolor{red}{excitation degree} while keeping a low \textcolor{red}{seniority number}).
In this sense, we hope to recover dynamic correlation by moving right in the map (increasing the seniority number while keeping a low excitation degree),
at the same time as static correlation, by moving down (increasing the excitation degree while keeping a low seniority number).
The second justification is computational.
In the hCI class of methods, each level of theory accommodates additional determinants from different excitation-seniority sectors (each block of same color tone in Fig.~\ref{fig:allCI}).